Finite-β minimum energy status of a two-fluid flowing plasma

The minimum energy theory of an ideal one-fluid plasma with invariant magnetic helicity, KB = ∫dτ A circ ∇xA, leads to the familiar Taylor states. A more general plasma model is an ideal two-fluid flowing system of ions and electrons. A reasonable extension of KB in such a medium is to replace A by the canonical momenta (using the specie flow velocity). The generalized helicities, one for each specie, are invariant in an ideal two-fluid plasma. If one postulates that both helicities are also invariant in a turbulent relaxation, then a pragmatic theory of minimum energy states can be developed, i.e. one that is verified a posteriori by comparison with laboratory plasmas. Essential features of these equilibria are sheared flows and finite β, both of which are absent in Taylor states. Adopting simplified geometries a range of equilibria are computed. These reproduce striking qualitative features observed in laboratory plasmas: FRC-like states exhibit hollow current profile, and a sharp density gradient at the edge; and tokamak-like states exhibit reversed magnetic shear, hollow current profile, and sheared toroidal flows